City Savers

There are N+1 towns. The i-th town is being attacked by A_i monsters.

We have N heroes. The i-th hero can defeat monsters attacking the i-th or (i+1)-th town, for a total of at most B_i monsters.

What is the maximum total number of monsters the heroes can cooperate to defeat?

Constraints

• All values in input are integers.
• 1 \leq N \leq 10^5
• 1 \leq A_i \leq 10^9
• 1 \leq B_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N A_1 A_2 ... A_{N+1} B_1 B_2 ... B_N

Output

Print the maximum total number of monsters the heroes can defeat.

Examples

Input

2 3 5 2 4 5

Output

9

Input

3 5 6 3 8 5 100 8

Output

22

Input

2 100 1 1 1 100

Output

3

inputFormat

input are integers.

• 1 \leq N \leq 10^5
• 1 \leq A_i \leq 10^9
• 1 \leq B_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N A_1 A_2 ... A_{N+1} B_1 B_2 ... B_N

outputFormat

Output

Print the maximum total number of monsters the heroes can defeat.

Examples

Input

2 3 5 2 4 5

Output

9

Input

3 5 6 3 8 5 100 8

Output

22

Input

2 100 1 1 1 100

Output

3

样例

3
5 6 3 8
5 100 8

22